June 1, 2009
OC Big Idea: Many real world situations can be modeled and predicted using mathematics.
Essential Question: How can I use math symbols to describe a pattern?
The table below gives equations for the relationships between the length of each bone and the height for males and females. These relationships were found by scientists after much study and data collection. In the table, F represents the length of the femur, T the length of the tibia, H the length of the humerus, R the length of the radius, and h the person’s height. All measurements are in centimeters.
Bone
Male
Female
Femur
h = 69.089 + 2.238F
h = 61.412 + 2.317F
Tibia
h=81.688 + 2.392T=
h 72.572 + 2.533T
Humerus
h=73.570 + 2.970H=
h 64.977 + 3.144H
Radius
h=80.405 + 3.650R=
h 73.502 + 3.876R
Use the equations above to answer parts A-D A. How tall is a female if her femur is 46.2 centimeters long? A female is approximately 168.4574 centimeters tall.
B. How tall is a male if his tibia is 50.1 centimeters long? A male is approximately 201.5272 centimeters tall.
C. If a woman is 152 centimeters (about 5 feet) tall, how long is her femur? Her tibia? Her humerus? Her radius? If a woman is 152 centimeters tall, her femur is approximately 37.04691689… centimeters long. Her tibia is approximately 31.35728385… centimeters long. Her humerus is approximately 27.679707125… centimeters long. Her radius is approximately 20.25232198… centimeters long.
D. If a man is 183 centimeters (about 6 feet) tall, how long is his femur? His tibia? His humerus? His radius? If a man is 183 centimeters tall, his femur is approximately 50.89857015… centimeters long. His tibia is approximately 42.35451505… centimeters long. His humerus is approximately 36.84511785… centimeters long. His radius is approximately 28.10821918… centimeters long.
Man: red, Women: green
Femur
Tibia
Humerus Radius
Problem 4.3 Follow-Up For one of the bones discussed above, graph the equations for males and females on the same set of axes. What do the x- and y-intercepts represent in terms of this problem? Does this make sense? Why? The x- and y- intercepts represents where the graph line meets the x and y axis. It doesn’t make sense because it doesn’t mean anything that important.
OC
Big Idea: Many real world situations can be modeled and predicted using mathematics.
Essential Question: How can I use math symbols to describe a pattern?
The table below gives equations for the relationships between the length of each bone and the height for males and females. These relationships were found by scientists after much study and data collection. In the table, F represents the length of the femur, T the length of the tibia, H the length of the humerus, R the length of the radius, and h the person’s height. All measurements are in centimeters.
Use the equations above to answer parts A-D
A. How tall is a female if her femur is 46.2 centimeters long?
A female is approximately 168.4574 centimeters tall.
B. How tall is a male if his tibia is 50.1 centimeters long?
A male is approximately 201.5272 centimeters tall.
C. If a woman is 152 centimeters (about 5 feet) tall, how long is her femur? Her tibia? Her humerus? Her radius?
If a woman is 152 centimeters tall, her femur is approximately 37.04691689… centimeters long. Her tibia is approximately 31.35728385… centimeters long. Her humerus is approximately 27.679707125… centimeters long. Her radius is approximately 20.25232198… centimeters long.
D. If a man is 183 centimeters (about 6 feet) tall, how long is his femur? His tibia? His humerus? His radius?
If a man is 183 centimeters tall, his femur is approximately 50.89857015… centimeters long. His tibia is approximately 42.35451505… centimeters long. His humerus is approximately 36.84511785… centimeters long. His radius is approximately 28.10821918… centimeters long.
Man: red, Women: green
Femur
Tibia
Humerus
Radius
Problem 4.3 Follow-Up
For one of the bones discussed above, graph the equations for males and females on the same set of axes. What do the x- and y-intercepts represent in terms of this problem? Does this make sense? Why?
The x- and y- intercepts represents where the graph line meets the x and y axis. It doesn’t make sense because it doesn’t mean anything that important.